Preprint (PDF) June 2014

American Mathematical Monthly**122** No 6 (2015), 592

Original article available at doi:10.4169/amer.math.monthly.122.6.592

American Mathematical Monthly

Original article available at doi:10.4169/amer.math.monthly.122.6.592

(This is intended as a classroom note) We give a direct proof of the fact that a continuous function on a compact metric space is automatically uniformly continuous. The proof is based on standard theorems from metric spaces: The inverse image of a closed set under a continuous function is continuous, the product of two compact metric spaces is compact, and every real valued continuous function attains a minimum on a compact set.

A preprint (PDF) is available or you can go to the original article.

**AMS Subject Classification (2000):**
54C05, 26A15